Non-linear supersymmetry and TT¯-like flows

TT ̄ deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain N = (2,2) models in two dimensions, where we observe an intriguing similarity with known N = 1 models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from T T ̄-like flow equations. We show that in four dimensions this is indeed the case for N = 1 Born-Infeld theory, as well as for the Goldstino action for spontaneously broken N = 1 supersymmetry.